A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

v1.1 update: Theorem 3.1 restructured to explicitly separate the conditional step (Weil explicit formula under RH) from the unconditional step (Backlund-Littlewood density estimate). Remark 3.3 added declaring the remaining open step: proving the uniform bound unconditionally without invoking RH. No mathematical content changed; the argument structure is now fully transparent.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20672043
Primary Topic
Mathematical and Theoretical Analysis
Type
preprint
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preprint

A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

Ariel Fernando Martini
Zenodo (CERN European Organization for Nuclear Research)
Mathematical and Theoretical Analysis
preprint

A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

Ariel Fernando Martini
preprint en

Abstract

v1.1 update: Theorem 3.1 restructured to explicitly separate the conditional step (Weil explicit formula under RH) from the unconditional step (Backlund-Littlewood density estimate). Remark 3.3 added declaring the remaining open step: proving the uniform bound unconditionally without invoking RH. No mathematical content changed; the argument structure is now fully transparent.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Mathematical and Theoretical Analysis
DOIOpen Access PDFOpenAlex
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A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero — Ariel Fernando Martini · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS